//931. 下降路径最小和--动规

class Solution {
public:
    int minFallingPathSum(vector<vector<int>>& matrix) {
        int m = matrix.size();
        int n = matrix[0].size();
        vector<vector<int>> dp(m + 1, vector<int>(n + 2, INT_MAX));
        for(int i = 0; i < m + 1; i++)
        {
            dp[0][i] = 0;
        }
        for(int i = 1; i <= m; i++)
        {
            for(int j = 1; j <= n; j++)
            {
                dp[i][j] = min(dp[i - 1][j - 1], min(dp[i - 1][j], dp[i - 1][j + 1])) +  matrix[i - 1][j - 1];
            }
        }
        int ret = INT_MAX;
        for(int j = 1; j < n + 1; j ++)
        {
            if(dp[m][j] < ret)
                ret = dp[m][j];
        }
        return ret;
    }
};